Applied Mathematics

Calculus

Easy

applied

If $R(x)$ is the total revenue received and $C(x)$ is the total cost incurred in the production of x units of a commodity, then the profit function $P(x)$

$P(x)=R(x)$

$P(x)=C(x)+R(x)$

$P(x)=\frac{R(x)}{C(x)}$

$P(x)=R(x)-C(x)$

✅ Correct Option: 4

Profit is what remains after costs are met, so $P(x)=R(x)-C(x)$ .

Differentiating this relation also gives marginal profit as marginal revenue minus marginal cost.

2023: 11 Aug Shift 1

The second order derivative of which of the following functions is $5^x$ ?

2023: 30 May Shift 3

If $C(x) = ax^2 - bx - c$ represents the total cost function then the slope of the tangent to the marginal cost curve at the point $(x, y)$ is :

2023: 23 May Shift 3

Two positive numbers $x$ and $y$ such that $x + y = 60$ and $xy^3$ is maximum are :

2023: 7 June Shift 1

If $t = e^{2x}$ and $\log_e t^2$ , then $\frac{d^2y}{dx^2}$ is :

2026: 14 May Shift 2

Match the LIST-I with LIST-II

	LIST-I (Differential equation)		LIST-II (Degree)
A.	$\left(\dfrac{dy}{dx}\right)^2 + \dfrac{1}{\dfrac{dy}{dx}} = 5$	I.	$2$
B.	$\dfrac{d^3y}{dx^3} = \left\{3 + \left(\dfrac{dy}{dx}\right)^2\right\}^{3/2}$	II.	$4$
C.	$\dfrac{d^2y}{dx^2} = \left(\dfrac{dy}{dx}\right)^{5/4}$	III.	$1$
D.	$y\dfrac{d^2x}{dy^2} = y^2 + 1$	IV.	$3$

Choose the correct answer from the options given below:

2026: 29 May Shift 2

The marginal cost (MC) of producing x units of an item in a factory is given by $MC=0.006x^2-0.001x+4$ .

If the fixed cost is ₹1000, then the cost of producing 200 units will be :

If R(x)R(x)R(x) is the total revenue received and C(x)C(x)C(x) is the total cost incurred in the production of x units of a commodity, then the profit function P(x)P(x)P(x)